%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP139^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:31 AM UTC 2026
% Result : Theorem 0.61s 0.43s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP139^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n009.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:59:30 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.43 % (279117)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.43 % (279126)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=892282139:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.43 % (279128)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.43 % (279128)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.61/0.43 % (279122)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2837909094:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.43 % (279126)Instruction limit reached!
% 0.61/0.43 % (279126)------------------------------
% 0.61/0.43 % (279126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279126)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279126)Termination reason: Instruction limit
% 0.61/0.43 % (279126)Termination phase: Property scanning
% 0.61/0.43 % (279126)Time elapsed: 0.006 s
% 0.61/0.43 % (279126)Peak memory usage: 10 MB
% 0.61/0.43 % (279126)Instructions burned: 27 (million)
% 0.61/0.43 % (279124)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=210281814:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.43 % (279128)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3022167881:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.43 % (279125)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3945423984:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.61/0.43 % (279127)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3779482267:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.43 % (279124)Instruction limit reached!
% 0.61/0.43 % (279124)------------------------------
% 0.61/0.43 % (279124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279124)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279124)Termination reason: Instruction limit
% 0.61/0.43 % (279124)Termination phase: shuffling
% 0.61/0.43 % (279124)Time elapsed: 0.002 s
% 0.61/0.43 % (279124)Peak memory usage: 10 MB
% 0.61/0.43 % (279124)Instructions burned: 3 (million)
% 0.61/0.43 % (279132)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=695103096:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.43 % (279132)Instruction limit reached!
% 0.61/0.43 % (279132)------------------------------
% 0.61/0.43 % (279132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279132)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279132)Termination reason: Instruction limit
% 0.61/0.43 % (279132)Termination phase: shuffling
% 0.61/0.43 % (279132)Time elapsed: 0.001 s
% 0.61/0.43 % (279132)Peak memory usage: 10 MB
% 0.61/0.43 % (279132)Instructions burned: 4 (million)
% 0.61/0.43 % (279123)lrs+10_16_si=on:nwc=1.5:random_seed=1242562746:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.43 % (279136)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=802980542:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.43 % (279139)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.43 % (279139)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=265772299:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.43 % (279136)Instruction limit reached!
% 0.61/0.43 % (279136)------------------------------
% 0.61/0.43 % (279136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279136)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279136)Termination reason: Instruction limit
% 0.61/0.43 % (279136)Termination phase: shuffling
% 0.61/0.43 % (279136)Time elapsed: 0.003 s
% 0.61/0.43 % (279136)Peak memory usage: 10 MB
% 0.61/0.43 % (279136)Instructions burned: 5 (million)
% 0.61/0.43 % (279139)Instruction limit reached!
% 0.61/0.43 % (279139)------------------------------
% 0.61/0.43 % (279139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279139)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279139)Termination reason: Instruction limit
% 0.61/0.43 % (279139)Termination phase: shuffling
% 0.61/0.43 % (279139)Time elapsed: 0.002 s
% 0.61/0.43 % (279139)Peak memory usage: 10 MB
% 0.61/0.43 % (279139)Instructions burned: 8 (million)
% 0.61/0.43 % (279123)Instruction limit reached!
% 0.61/0.43 % (279123)------------------------------
% 0.61/0.43 % (279123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279123)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279123)Termination reason: Instruction limit
% 0.61/0.43 % (279123)Termination phase: shuffling
% 0.61/0.43 % (279123)Time elapsed: 0.015 s
% 0.61/0.43 % (279123)Peak memory usage: 10 MB
% 0.61/0.43 % (279123)Instructions burned: 18 (million)
% 0.61/0.43 % (279127)Instruction limit reached!
% 0.61/0.43 % (279127)------------------------------
% 0.61/0.43 % (279127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279127)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279127)Termination reason: Instruction limit
% 0.61/0.43 % (279127)Termination phase: Property scanning
% 0.61/0.43 % (279127)Time elapsed: 0.037 s
% 0.61/0.43 % (279127)Peak memory usage: 12 MB
% 0.61/0.43 % (279127)Instructions burned: 78 (million)
% 0.61/0.43 % (279143)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.61/0.43 % (279143)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.43 % (279122)Instruction limit reached!
% 0.61/0.43 % (279122)------------------------------
% 0.61/0.43 % (279122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279122)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279122)Termination reason: Instruction limit
% 0.61/0.43 % (279122)Termination phase: Property scanning
% 0.61/0.43 % (279122)Time elapsed: 0.041 s
% 0.61/0.43 % (279122)Peak memory usage: 12 MB
% 0.61/0.43 % (279122)Instructions burned: 89 (million)
% 0.61/0.43 % (279143)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2467933523:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.43 % (279143)Instruction limit reached!
% 0.61/0.43 % (279143)------------------------------
% 0.61/0.43 % (279143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279143)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279143)Termination reason: Instruction limit
% 0.61/0.43 % (279143)Termination phase: shuffling
% 0.61/0.43 % (279143)Time elapsed: 0.007 s
% 0.61/0.43 % (279143)Peak memory usage: 10 MB
% 0.61/0.43 % (279143)Instructions burned: 28 (million)
% 0.61/0.43 % (279144)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2879661197:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.43 % (279147)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.43 % (279145)lrs+10_1_si=on:cs=on:random_seed=2305956874:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.43 % (279142)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2561332798:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.43 % (279147)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1882311408:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.43 % (279147)Instruction limit reached!
% 0.61/0.43 % (279147)------------------------------
% 0.61/0.43 % (279147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279147)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279147)Termination reason: Instruction limit
% 0.61/0.43 % (279147)Termination phase: shuffling
% 0.61/0.43 % (279147)Time elapsed: 0.002 s
% 0.61/0.43 % (279147)Peak memory usage: 10 MB
% 0.61/0.43 % (279147)Instructions burned: 3 (million)
% 0.61/0.43 % (279145)Instruction limit reached!
% 0.61/0.43 % (279145)------------------------------
% 0.61/0.43 % (279145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279145)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279145)Termination reason: Instruction limit
% 0.61/0.43 % (279145)Termination phase: shuffling
% 0.61/0.43 % (279145)Time elapsed: 0.004 s
% 0.61/0.43 % (279145)Peak memory usage: 10 MB
% 0.61/0.43 % (279145)Instructions burned: 8 (million)
% 0.61/0.43 % (279148)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3052302720:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.61/0.43 % (279142)Instruction limit reached!
% 0.61/0.43 % (279142)------------------------------
% 0.61/0.43 % (279142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279142)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279142)Termination reason: Instruction limit
% 0.61/0.43 % (279142)Termination phase: shuffling
% 0.61/0.43 % (279142)Time elapsed: 0.010 s
% 0.61/0.43 % (279142)Peak memory usage: 10 MB
% 0.61/0.43 % (279142)Instructions burned: 12 (million)
% 0.61/0.43 % (279128)Instruction limit reached!
% 0.61/0.43 % (279128)------------------------------
% 0.61/0.43 % (279128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279128)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279128)Termination reason: Instruction limit
% 0.61/0.43 % (279128)Termination phase: Saturation
% 0.61/0.43 % (279128)Time elapsed: 0.068 s
% 0.61/0.43 % (279128)Peak memory usage: 14 MB
% 0.61/0.43 % (279128)Instructions burned: 158 (million)
% 0.61/0.43 % (279144)Instruction limit reached!
% 0.61/0.43 % (279144)------------------------------
% 0.61/0.43 % (279144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279144)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279144)Termination reason: Instruction limit
% 0.61/0.43 % (279144)Termination phase: Preprocessing 2
% 0.61/0.43 % (279144)Time elapsed: 0.019 s
% 0.61/0.43 % (279144)Peak memory usage: 11 MB
% 0.61/0.43 % (279144)Instructions burned: 86 (million)
% 0.61/0.43 % (279157)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=647967151:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.43 % (279153)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3438021227:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.43 % (279154)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=567747470:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.43 % (279125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-279117-279125"...
% 0.61/0.43 % (279148)Instruction limit reached!
% 0.61/0.43 % (279148)------------------------------
% 0.61/0.43 % (279148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (279148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (279148)CaDiCaL version: 2.1.3
% 0.61/0.43 % (279148)Termination reason: Instruction limit
% 0.61/0.43 % (279148)Termination phase: Property scanning
% 0.61/0.43 % (279148)Time elapsed: 0.017 s
% 0.61/0.43 % (279148)Peak memory usage: 11 MB
% 0.61/0.43 % (279148)Instructions burned: 39 (million)
% 0.61/0.43 % (279125)...printing done.
% 0.61/0.43 % (279156)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=380512950:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.43 % (279158)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=351086031:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.43 % (279125)Refutation found. Thanks to Tanya!
% 0.61/0.43 % SZS status Theorem for theBenchmark
% 0.61/0.43 % SZS output start Proof for theBenchmark
% 0.61/0.43 thf(type_def_5, type, set_Pr2014382200lle_tv: $tType).
% 0.61/0.43 thf(type_def_6, type, produc1647334210lle_tv: $tType).
% 0.61/0.43 thf(type_def_7, type, set_Pr1725653840tv_nat: $tType).
% 0.61/0.43 thf(type_def_8, type, set_Pr13445366lle_tv: $tType).
% 0.61/0.43 thf(type_def_9, type, produc194167194tv_nat: $tType).
% 0.61/0.43 thf(type_def_10, type, produc270694976lle_tv: $tType).
% 0.61/0.43 thf(type_def_11, type, set_se800614875lle_tv: $tType).
% 0.61/0.43 thf(type_def_12, type, set_Pr1986765409at_nat: $tType).
% 0.61/0.43 thf(type_def_13, type, set_Pa1764573435lle_tv: $tType).
% 0.61/0.43 thf(type_def_14, type, product_prod_nat_nat: $tType).
% 0.61/0.43 thf(type_def_15, type, paraco1605129243lle_tv: $tType).
% 0.61/0.43 thf(type_def_16, type, set_set_nat: $tType).
% 0.61/0.43 thf(type_def_17, type, set_nat: $tType).
% 0.61/0.43 thf(type_def_18, type, nat: $tType).
% 0.61/0.43 thf(type_def_19, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.43 thf(func_def_0, type, inj_on_nat_nat: ((nat > nat) > set_nat > $o)).
% 0.61/0.43 thf(func_def_1, type, inj_on1955349912lle_tv: ((nat > paraco1605129243lle_tv) > set_nat > $o)).
% 0.61/0.43 thf(func_def_2, type, inj_on1179712058tv_nat: ((paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > $o)).
% 0.61/0.43 thf(func_def_3, type, inj_on772319074lle_tv: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > $o)).
% 0.61/0.43 thf(func_def_4, type, inj_on642995232at_nat: ((product_prod_nat_nat > nat) > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_5, type, inj_on520021963lle_tv: ((product_prod_nat_nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_6, type, inj_on26176689at_nat: ((product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_7, type, inj_on1840679568lle_tv: ((product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_8, type, inj_on1764151786tv_nat: ((product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_9, type, inj_on936843139tv_nat: ((produc270694976lle_tv > nat) > set_Pr13445366lle_tv > $o)).
% 0.61/0.43 thf(func_def_10, type, inj_on394919723lle_tv: ((produc270694976lle_tv > paraco1605129243lle_tv) > set_Pr13445366lle_tv > $o)).
% 0.61/0.43 thf(func_def_11, type, inj_on1954136462at_nat: ((produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > $o)).
% 0.61/0.43 thf(func_def_12, type, inj_on1745913142lle_tv: ((produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > $o)).
% 0.61/0.43 thf(func_def_13, type, inj_on808253149at_nat: ((produc194167194tv_nat > nat) > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_14, type, inj_on1612474245lle_tv: ((produc194167194tv_nat > paraco1605129243lle_tv) > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_15, type, inj_on1971554740at_nat: ((produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_16, type, inj_on552895452tv_nat: ((produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_17, type, inj_on967082628lle_tv: ((produc194167194tv_nat > produc1647334210lle_tv) > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_18, type, inj_on2112487900lle_tv: ((produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > $o)).
% 0.61/0.43 thf(func_def_19, type, strict2146030304at_nat: ((nat > nat) > set_nat > $o)).
% 0.61/0.43 thf(func_def_20, type, strict1310998166et_nat: ((nat > set_nat) > set_nat > $o)).
% 0.61/0.43 thf(func_def_21, type, strict1658340843lle_tv: ((nat > set_Pa1764573435lle_tv) > set_nat > $o)).
% 0.61/0.43 thf(func_def_22, type, strict1802283670at_nat: ((set_nat > nat) > set_set_nat > $o)).
% 0.61/0.43 thf(func_def_23, type, strict473775692et_nat: ((set_nat > set_nat) > set_set_nat > $o)).
% 0.61/0.43 thf(func_def_24, type, strict172559285lle_tv: ((set_nat > set_Pa1764573435lle_tv) > set_set_nat > $o)).
% 0.61/0.43 thf(func_def_25, type, strict1125660301tv_nat: ((set_Pa1764573435lle_tv > nat) > set_se800614875lle_tv > $o)).
% 0.61/0.43 thf(func_def_26, type, strict1455779395et_nat: ((set_Pa1764573435lle_tv > set_nat) > set_se800614875lle_tv > $o)).
% 0.61/0.43 thf(func_def_27, type, strict592849515lle_tv: ((set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_se800614875lle_tv > $o)).
% 0.61/0.43 thf(func_def_28, type, the_inv_into_nat_nat: (set_nat > (nat > nat) > nat > nat)).
% 0.61/0.43 thf(func_def_29, type, the_in138087638lle_tv: (set_nat > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > nat)).
% 0.61/0.43 thf(func_def_30, type, the_in1509933432tv_nat: (set_Pa1764573435lle_tv > (paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_31, type, the_in452116896lle_tv: (set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_32, type, the_in2068894451at_nat: (set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_33, type, the_in744013006lle_tv: (set_Pr1986765409at_nat > (product_prod_nat_nat > produc270694976lle_tv) > produc270694976lle_tv > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_34, type, the_in667485224tv_nat: (set_Pr1986765409at_nat > (product_prod_nat_nat > produc194167194tv_nat) > produc194167194tv_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_35, type, the_in857469900at_nat: (set_Pr13445366lle_tv > (produc270694976lle_tv > product_prod_nat_nat) > product_prod_nat_nat > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_36, type, the_in1388677748lle_tv: (set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_37, type, the_in874888178at_nat: (set_Pr1725653840tv_nat > (produc194167194tv_nat > product_prod_nat_nat) > product_prod_nat_nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_38, type, the_in195660058tv_nat: (set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_39, type, the_in427240730lle_tv: (set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_40, type, plus_plus_nat: (nat > nat > nat)).
% 0.61/0.43 thf(func_def_41, type, ord_less_nat: (nat > nat > $o)).
% 0.61/0.43 thf(func_def_42, type, ord_less_set_nat: (set_nat > set_nat > $o)).
% 0.61/0.43 thf(func_def_43, type, ord_le727057319lle_tv: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o)).
% 0.61/0.43 thf(func_def_44, type, ord_less_eq_nat: (nat > nat > $o)).
% 0.61/0.43 thf(func_def_45, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 0.61/0.43 thf(func_def_46, type, ord_le241064091lle_tv: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o)).
% 0.61/0.43 thf(func_def_47, type, order_769474267at_nat: ((nat > nat) > $o)).
% 0.61/0.43 thf(func_def_48, type, top_top_nat_o: (nat > $o)).
% 0.61/0.43 thf(func_def_49, type, top_to1299250770e_tv_o: (paraco1605129243lle_tv > $o)).
% 0.61/0.43 thf(func_def_50, type, top_to632227436_nat_o: (product_prod_nat_nat > $o)).
% 0.61/0.43 thf(func_def_51, type, top_to1889334367e_tv_o: (produc270694976lle_tv > $o)).
% 0.61/0.43 thf(func_def_52, type, top_to900819589_nat_o: (produc194167194tv_nat > $o)).
% 0.61/0.43 thf(func_def_53, type, top_top_o: $o).
% 0.61/0.43 thf(func_def_54, type, top_top_set_nat: set_nat).
% 0.61/0.43 thf(func_def_55, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 0.61/0.43 thf(func_def_56, type, top_to1555900337at_nat: set_Pr1986765409at_nat).
% 0.61/0.43 thf(func_def_57, type, top_to1411004326lle_tv: set_Pr13445366lle_tv).
% 0.61/0.43 thf(func_def_58, type, top_to975729152tv_nat: set_Pr1725653840tv_nat).
% 0.61/0.43 thf(func_def_59, type, top_to1871154984lle_tv: set_Pr2014382200lle_tv).
% 0.61/0.43 thf(func_def_60, type, paraco1147068288nge_tv: ((nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_61, type, paraco793048302_Indet: (nat > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_62, type, produc1320959600at_nat: ((nat > nat) > product_prod_nat_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_63, type, produc237097339lle_tv: ((nat > nat) > produc194167194tv_nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_64, type, produc1608943133tv_nat: ((nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_65, type, produc1804670661lle_tv: ((nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_66, type, produc2040316391tv_nat: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_67, type, produc1408152463lle_tv: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_68, type, produc505105722at_nat: ((nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_69, type, produc2101297531lle_tv: ((nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_70, type, produc189459613tv_nat: ((nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_71, type, produc1975500101lle_tv: ((nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_72, type, produc386540311at_nat: ((paraco1605129243lle_tv > nat) > (nat > nat) > produc194167194tv_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_73, type, produc72207551lle_tv: ((paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_74, type, produc51277375tv_nat: ((paraco1605129243lle_tv > nat) > (paraco1605129243lle_tv > nat) > produc1647334210lle_tv > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_75, type, produc1095080935lle_tv: ((paraco1605129243lle_tv > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_76, type, produc42536895at_nat: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > nat) > produc194167194tv_nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_77, type, produc1521089895lle_tv: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_78, type, produc1500159719tv_nat: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc1647334210lle_tv > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_79, type, produc1345917071lle_tv: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_80, type, collect_nat: ((nat > $o) > set_nat)).
% 0.61/0.43 thf(func_def_81, type, collec1111687558lle_tv: ((paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_82, type, collec7649004at_nat: ((product_prod_nat_nat > $o) > set_Pr1986765409at_nat)).
% 0.61/0.43 thf(func_def_83, type, collec924990229lle_tv: ((produc270694976lle_tv > $o) > set_Pr13445366lle_tv)).
% 0.61/0.43 thf(func_def_84, type, collec848462447tv_nat: ((produc194167194tv_nat > $o) > set_Pr1725653840tv_nat)).
% 0.61/0.43 thf(func_def_85, type, image_nat_nat: ((nat > nat) > set_nat > set_nat)).
% 0.61/0.43 thf(func_def_86, type, image_1151963140lle_tv: ((nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_87, type, image_376325286tv_nat: ((paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat)).
% 0.61/0.43 thf(func_def_88, type, image_335818702lle_tv: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_89, type, image_1397137548at_nat: ((product_prod_nat_nat > nat) > set_Pr1986765409at_nat > set_nat)).
% 0.61/0.43 thf(func_def_90, type, image_1093035615lle_tv: ((product_prod_nat_nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_91, type, image_815163717at_nat: ((product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > set_Pr1986765409at_nat)).
% 0.61/0.43 thf(func_def_92, type, image_1674248956lle_tv: ((product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > set_Pr13445366lle_tv)).
% 0.61/0.43 thf(func_def_93, type, image_1597721174tv_nat: ((product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat)).
% 0.61/0.43 thf(func_def_94, type, image_1509856791tv_nat: ((produc270694976lle_tv > nat) > set_Pr13445366lle_tv > set_nat)).
% 0.61/0.43 thf(func_def_95, type, image_802013119lle_tv: ((produc270694976lle_tv > paraco1605129243lle_tv) > set_Pr13445366lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_96, type, image_1787705850at_nat: ((produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > set_Pr1986765409at_nat)).
% 0.61/0.43 thf(func_def_97, type, image_149830562lle_tv: ((produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > set_Pr13445366lle_tv)).
% 0.61/0.43 thf(func_def_98, type, image_53754658tv_nat: ((produc270694976lle_tv > produc194167194tv_nat) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat)).
% 0.61/0.43 thf(func_def_99, type, image_988201162lle_tv: ((produc270694976lle_tv > produc1647334210lle_tv) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv)).
% 0.61/0.43 thf(func_def_100, type, image_1381266801at_nat: ((produc194167194tv_nat > nat) > set_Pr1725653840tv_nat > set_nat)).
% 0.61/0.43 thf(func_def_101, type, image_2019567641lle_tv: ((produc194167194tv_nat > paraco1605129243lle_tv) > set_Pr1725653840tv_nat > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_102, type, image_1805124128at_nat: ((produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat)).
% 0.61/0.43 thf(func_def_103, type, image_1200372424lle_tv: ((produc194167194tv_nat > produc270694976lle_tv) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv)).
% 0.61/0.43 thf(func_def_104, type, image_1104296520tv_nat: ((produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > set_Pr1725653840tv_nat)).
% 0.61/0.43 thf(func_def_105, type, image_228488944lle_tv: ((produc194167194tv_nat > produc1647334210lle_tv) > set_Pr1725653840tv_nat > set_Pr2014382200lle_tv)).
% 0.61/0.43 thf(func_def_106, type, image_901203832at_nat: ((produc1647334210lle_tv > product_prod_nat_nat) > set_Pr2014382200lle_tv > set_Pr1986765409at_nat)).
% 0.61/0.43 thf(func_def_107, type, image_1892891680lle_tv: ((produc1647334210lle_tv > produc270694976lle_tv) > set_Pr2014382200lle_tv > set_Pr13445366lle_tv)).
% 0.61/0.43 thf(func_def_108, type, image_1796815776tv_nat: ((produc1647334210lle_tv > produc194167194tv_nat) > set_Pr2014382200lle_tv > set_Pr1725653840tv_nat)).
% 0.61/0.43 thf(func_def_109, type, image_1221801032lle_tv: ((produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv)).
% 0.61/0.43 thf(func_def_110, type, member_nat: (nat > set_nat > $o)).
% 0.61/0.43 thf(func_def_111, type, member266900804lle_tv: (paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o)).
% 0.61/0.43 thf(func_def_112, type, member701585322at_nat: (product_prod_nat_nat > set_Pr1986765409at_nat > $o)).
% 0.61/0.43 thf(func_def_113, type, member813679063lle_tv: (produc270694976lle_tv > set_Pr13445366lle_tv > $o)).
% 0.61/0.43 thf(func_def_114, type, member737151281tv_nat: (produc194167194tv_nat > set_Pr1725653840tv_nat > $o)).
% 0.61/0.43 thf(func_def_115, type, member1531318361lle_tv: (produc1647334210lle_tv > set_Pr2014382200lle_tv > $o)).
% 0.61/0.43 thf(func_def_116, type, member_set_nat: (set_nat > set_set_nat > $o)).
% 0.61/0.43 thf(func_def_117, type, member1875402276lle_tv: (set_Pa1764573435lle_tv > set_se800614875lle_tv > $o)).
% 0.61/0.43 thf(func_def_118, type, f: (nat > nat)).
% 0.61/0.43 thf(func_def_122, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.43 thf(func_def_123, type, vIMP: ($o > $o > $o)).
% 0.61/0.43 thf(func_def_124, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.43 thf(func_def_125, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.43 thf(func_def_126, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.43 thf(func_def_127, type, db3: !>[X0: $tType]:(X0)).
% 0.61/0.43 thf(func_def_128, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.43 thf(func_def_129, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.43 thf(func_def_130, type, vAND: ($o > $o > $o)).
% 0.61/0.43 thf(func_def_131, type, sK0: (set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_132, type, sK1: ((produc270694976lle_tv > produc270694976lle_tv) > (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_133, type, sK2: produc194167194tv_nat).
% 0.61/0.43 thf(func_def_134, type, sK3: (produc270694976lle_tv > (produc270694976lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_135, type, sK4: ((produc270694976lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_136, type, sK5: ((paraco1605129243lle_tv > nat) > set_nat > set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_137, type, sK6: (set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_138, type, sK7: ((produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_139, type, sK8: ((product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_140, type, sK9: ((product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_141, type, sK10: ((produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_142, type, sK11: ((produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_143, type, sK12: (nat > (product_prod_nat_nat > nat) > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_144, type, sK13: (product_prod_nat_nat > nat > (product_prod_nat_nat > nat) > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_145, type, sK14: (set_nat > (nat > set_nat) > nat)).
% 0.61/0.43 thf(func_def_146, type, sK15: (set_nat > (nat > set_nat) > nat)).
% 0.61/0.43 thf(func_def_147, type, sK16: ((nat > nat) > set_nat > nat)).
% 0.61/0.43 thf(func_def_148, type, sK17: ((nat > nat) > set_nat > nat)).
% 0.61/0.43 thf(func_def_149, type, sK18: (set_nat > nat)).
% 0.61/0.43 thf(func_def_150, type, sK19: (set_set_nat > (set_nat > nat) > set_nat)).
% 0.61/0.43 thf(func_def_151, type, sK20: (set_set_nat > (set_nat > nat) > set_nat)).
% 0.61/0.43 thf(func_def_152, type, sK21: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_153, type, sK22: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_154, type, sK23: ((nat > nat) > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_155, type, sK24: ((paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_156, type, sK25: ((nat > nat) > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_157, type, sK26: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_158, type, sK27: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_159, type, sK28: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_160, type, sK29: (set_Pr1986765409at_nat > (produc194167194tv_nat > $o) > (product_prod_nat_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_161, type, sK30: nat).
% 0.61/0.43 thf(func_def_162, type, sK31: ((produc194167194tv_nat > nat) > nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_163, type, sK32: (produc194167194tv_nat > (produc194167194tv_nat > nat) > nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_164, type, sK33: product_prod_nat_nat).
% 0.61/0.43 thf(func_def_165, type, sK34: (set_nat > set_nat > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_166, type, sK35: ((set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_167, type, sK36: ((set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_168, type, sK37: ((produc270694976lle_tv > $o) > set_Pr1986765409at_nat > (product_prod_nat_nat > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.43 thf(func_def_169, type, sK38: (set_Pr1986765409at_nat > product_prod_nat_nat)).
% 0.61/0.43 thf(func_def_170, type, sK39: ((nat > set_nat) > nat)).
% 0.61/0.43 thf(func_def_171, type, sK40: ((nat > set_nat) > nat)).
% 0.61/0.43 thf(func_def_172, type, sK41: ((produc1647334210lle_tv > produc1647334210lle_tv) > (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_173, type, sK42: ((set_nat > set_Pa1764573435lle_tv) > set_nat)).
% 0.61/0.43 thf(func_def_174, type, sK43: ((set_nat > set_Pa1764573435lle_tv) > set_nat)).
% 0.61/0.43 thf(func_def_175, type, sK44: (set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_176, type, sK45: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_177, type, sK46: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_178, type, sK47: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_179, type, sK48: (set_nat > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_180, type, sK49: (set_nat > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_181, type, sK50: (paraco1605129243lle_tv > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_182, type, sK51: (nat > paraco1605129243lle_tv > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_183, type, sK52: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_184, type, sK53: ((nat > nat) > nat)).
% 0.61/0.43 thf(func_def_185, type, sK54: ((nat > set_Pa1764573435lle_tv) > set_nat > nat)).
% 0.61/0.43 thf(func_def_186, type, sK55: ((nat > set_Pa1764573435lle_tv) > set_nat > nat)).
% 0.61/0.43 thf(func_def_187, type, sK56: ((set_Pa1764573435lle_tv > nat) > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_188, type, sK57: ((set_Pa1764573435lle_tv > nat) > set_Pa1764573435lle_tv)).
% 0.61/0.43 thf(func_def_189, type, sK58: (set_nat > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_190, type, sK59: (set_nat > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_191, type, sK60: (set_nat > nat)).
% 0.61/0.43 thf(func_def_192, type, sK61: (set_nat > nat)).
% 0.61/0.43 thf(func_def_193, type, sK62: (set_nat > set_nat > nat)).
% 0.61/0.43 thf(func_def_194, type, sK63: ((nat > nat) > nat > nat)).
% 0.61/0.43 thf(func_def_195, type, sK64: ((nat > $o) > (nat > $o) > nat)).
% 0.61/0.43 thf(func_def_196, type, sK65: ((produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_197, type, sK66: ((produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.43 thf(func_def_198, type, sK67: ((paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_199, type, sK68: (paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_200, type, sK69: (paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_201, type, sK70: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_202, type, sK71: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_203, type, sK72: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.43 thf(func_def_204, type, sK73: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_205, type, sK74: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 0.61/0.43 thf(func_def_206, type, sK75: ((produc194167194tv_nat > produc194167194tv_nat) > (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > produc194167194tv_nat)).
% 0.61/0.43 thf(func_def_207, type, sK76: ((set_nat > nat) > set_nat)).
% 0.61/0.43 thf(func_def_208, type, sK77: ((set_nat > nat) > set_nat)).
% 0.61/0.43 thf(func_def_209, type, sK78: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_210, type, sK79: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.43 thf(func_def_211, type, sK80: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_212, type, sK81: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_213, type, sK82: (set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.44 thf(func_def_214, type, sK83: (set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.44 thf(func_def_215, type, sK84: (set_nat > (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > nat)).
% 0.61/0.44 thf(func_def_216, type, sK85: (produc270694976lle_tv > set_Pr1986765409at_nat > (product_prod_nat_nat > produc270694976lle_tv) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_217, type, sK86: (paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_218, type, sK87: (paraco1605129243lle_tv > paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_219, type, sK88: ((product_prod_nat_nat > $o) > set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_220, type, sK89: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_221, type, sK90: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_222, type, sK91: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_223, type, sK92: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_224, type, sK93: ((produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_225, type, sK94: ((produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_226, type, sK95: (nat > nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_227, type, sK96: (nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_228, type, sK97: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_229, type, sK98: ((product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_230, type, sK99: ((produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.44 thf(func_def_231, type, sK100: ((produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv)).
% 0.61/0.44 thf(func_def_232, type, sK101: ((set_nat > set_nat) > set_set_nat > set_nat)).
% 0.61/0.44 thf(func_def_233, type, sK102: ((set_nat > set_nat) > set_set_nat > set_nat)).
% 0.61/0.44 thf(func_def_234, type, sK103: (set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_235, type, sK104: (nat > (nat > nat) > set_nat > nat)).
% 0.61/0.44 thf(func_def_236, type, sK105: (nat > (paraco1605129243lle_tv > nat) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_237, type, sK106: (paraco1605129243lle_tv > nat > (paraco1605129243lle_tv > nat) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_238, type, sK107: (set_Pr1986765409at_nat > (product_prod_nat_nat > produc194167194tv_nat) > (product_prod_nat_nat > produc194167194tv_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_239, type, sK108: (nat > (produc270694976lle_tv > nat) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_240, type, sK109: (produc270694976lle_tv > nat > (produc270694976lle_tv > nat) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_241, type, sK110: ((paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_242, type, sK111: ((product_prod_nat_nat > produc270694976lle_tv) > (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_243, type, sK112: ((paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_244, type, sK113: ((set_Pa1764573435lle_tv > nat) > set_se800614875lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_245, type, sK114: ((set_Pa1764573435lle_tv > nat) > set_se800614875lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_246, type, sK115: (set_Pa1764573435lle_tv > set_nat > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_247, type, sK116: ((paraco1605129243lle_tv > $o) > set_nat > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_248, type, sK117: ((nat > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > set_nat > nat)).
% 0.61/0.44 thf(func_def_249, type, sK118: (set_nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_250, type, sK119: (set_nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_251, type, sK120: ((produc1647334210lle_tv > produc1647334210lle_tv) > (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > produc1647334210lle_tv)).
% 0.61/0.44 thf(func_def_252, type, sK121: ((nat > set_Pa1764573435lle_tv) > nat)).
% 0.61/0.44 thf(func_def_253, type, sK122: ((nat > set_Pa1764573435lle_tv) > nat)).
% 0.61/0.44 thf(func_def_254, type, sK123: ((paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_255, type, sK124: (set_Pr1725653840tv_nat > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_256, type, sK125: (set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_257, type, sK126: (set_se800614875lle_tv > (set_Pa1764573435lle_tv > set_nat) > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_258, type, sK127: (set_se800614875lle_tv > (set_Pa1764573435lle_tv > set_nat) > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_259, type, sK128: ((nat > nat) > nat)).
% 0.61/0.44 thf(func_def_260, type, sK129: ((nat > nat) > nat)).
% 0.61/0.44 thf(func_def_261, type, sK130: produc270694976lle_tv).
% 0.61/0.44 thf(func_def_262, type, sK131: ((product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > (produc194167194tv_nat > $o) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_263, type, sK132: ((produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_264, type, sK133: ((produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_265, type, sK134: ((product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > produc194167194tv_nat > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_266, type, sK135: ((paraco1605129243lle_tv > $o) > set_nat > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_267, type, sK136: ((product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_268, type, sK137: ((product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_269, type, sK138: ((product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_270, type, sK139: (set_Pr1986765409at_nat > (product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_271, type, sK140: ((nat > nat) > (nat > $o) > set_nat > nat)).
% 0.61/0.44 thf(func_def_272, type, sK141: ((nat > paraco1605129243lle_tv) > set_nat > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_273, type, sK142: (set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_274, type, sK143: (set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_275, type, sK144: paraco1605129243lle_tv).
% 0.61/0.44 thf(func_def_276, type, sK145: (set_set_nat > (set_nat > set_Pa1764573435lle_tv) > set_nat)).
% 0.61/0.44 thf(func_def_277, type, sK146: (set_set_nat > (set_nat > set_Pa1764573435lle_tv) > set_nat)).
% 0.61/0.44 thf(func_def_278, type, sK147: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_279, type, sK148: (product_prod_nat_nat > (product_prod_nat_nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_280, type, sK149: ((product_prod_nat_nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_281, type, sK150: (nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_282, type, sK151: ((nat > nat) > nat)).
% 0.61/0.44 thf(func_def_283, type, sK152: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_284, type, sK153: ((nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_285, type, sK154: (nat > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_286, type, sK155: (set_nat > (nat > nat) > set_nat > set_nat)).
% 0.61/0.44 thf(func_def_287, type, sK156: (set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_288, type, sK157: (set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_289, type, sK158: ((nat > paraco1605129243lle_tv) > set_nat > paraco1605129243lle_tv > nat)).
% 0.61/0.44 thf(func_def_290, type, sK159: ((produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_291, type, sK160: ((produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_292, type, sK161: ((nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > nat)).
% 0.61/0.44 thf(func_def_293, type, sK162: (nat > (paraco1605129243lle_tv > nat) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_294, type, sK163: ((paraco1605129243lle_tv > nat) > nat)).
% 0.61/0.44 thf(func_def_295, type, sK164: ((set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_se800614875lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_296, type, sK165: ((set_Pa1764573435lle_tv > set_Pa1764573435lle_tv) > set_se800614875lle_tv > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_297, type, sK166: ((nat > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_298, type, sK167: (paraco1605129243lle_tv > (nat > paraco1605129243lle_tv) > nat)).
% 0.61/0.44 thf(func_def_299, type, sK168: (set_Pr13445366lle_tv > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_300, type, sK169: ((nat > nat) > set_nat > (nat > $o) > nat)).
% 0.61/0.44 thf(func_def_301, type, sK170: (paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_302, type, sK171: ((nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > nat)).
% 0.61/0.44 thf(func_def_303, type, sK172: (produc194167194tv_nat > paraco1605129243lle_tv > (produc194167194tv_nat > paraco1605129243lle_tv) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_304, type, sK173: (paraco1605129243lle_tv > (produc194167194tv_nat > paraco1605129243lle_tv) > produc194167194tv_nat)).
% 0.61/0.44 thf(func_def_305, type, sK174: ((set_Pa1764573435lle_tv > set_nat) > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_306, type, sK175: ((set_Pa1764573435lle_tv > set_nat) > set_Pa1764573435lle_tv)).
% 0.61/0.44 thf(func_def_307, type, sK176: (set_Pr1986765409at_nat > product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_308, type, sK177: ((set_nat > set_nat) > set_nat)).
% 0.61/0.44 thf(func_def_309, type, sK178: ((set_nat > set_nat) > set_nat)).
% 0.61/0.44 thf(func_def_310, type, sK179: ((produc270694976lle_tv > $o) > set_Pr1986765409at_nat > (product_prod_nat_nat > produc270694976lle_tv) > product_prod_nat_nat)).
% 0.61/0.44 thf(func_def_311, type, sK180: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_312, type, sK181: ((paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv)).
% 0.61/0.44 thf(func_def_313, type, sK182: ((produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_314, type, sK183: ((produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv)).
% 0.61/0.44 thf(func_def_315, type, sK184: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 0.61/0.44 thf(func_def_316, type, vNOT: ($o > $o)).
% 0.61/0.44 thf(func_def_318, type, inv_paraco793048302_Indet_186: (paraco1605129243lle_tv > nat)).
% 0.61/0.44 thf(f1,axiom,(
% 0.61/0.44 ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) = ((paraco1147068288nge_tv @ f @ X1))) => (X0 = X1))),
% 0.61/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062)).
% 0.61/0.44 thf(f26,axiom,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : (! [X1 : paraco1605129243lle_tv,X2 : paraco1605129243lle_tv] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => (inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv))),
% 0.61/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_injI)).
% 0.61/0.44 thf(f356,conjecture,(
% 0.61/0.44 (inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 0.61/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.44 thf(f357,negated_conjecture,(
% 0.61/0.44 ~(inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 0.61/0.44 inference(negated_conjecture,[status(cth)],[f356])).
% 0.61/0.44 thf(f493,plain,(
% 0.61/0.44 ~(inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)),
% 0.61/0.44 inference(rectify,[],[f357])).
% 0.61/0.44 thf(f494,plain,(
% 0.61/0.44 ~ (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f493])).
% 0.61/0.44 thf(f854,plain,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : (! [X1 : paraco1605129243lle_tv,X2 : paraco1605129243lle_tv] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => (inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv))),
% 0.61/0.44 inference(rectify,[],[f26])).
% 0.61/0.44 thf(f855,plain,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : (! [X1 : paraco1605129243lle_tv,X2 : paraco1605129243lle_tv] : ((((X0 @ X1)) = ((X0 @ X2))) => (X1 = X2)) => (((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true))),
% 0.61/0.44 inference(fool_elimination,[],[f854])).
% 0.61/0.44 thf(f976,plain,(
% 0.61/0.44 (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) != $true)),
% 0.61/0.44 inference(flattening,[],[f494])).
% 0.61/0.44 thf(f1129,plain,(
% 0.61/0.44 ! [X1 : paraco1605129243lle_tv,X0 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) != ((paraco1147068288nge_tv @ f @ X1))) | (X0 = X1))),
% 0.61/0.44 inference(ennf_transformation,[],[f1])).
% 0.61/0.44 thf(f1280,plain,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : ((((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true) | ? [X2 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : ((((X0 @ X1)) = ((X0 @ X2))) & (X1 != X2)))),
% 0.61/0.44 inference(ennf_transformation,[],[f855])).
% 0.61/0.44 thf(f1479,plain,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : ((((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true) | ? [X1 : paraco1605129243lle_tv,X2 : paraco1605129243lle_tv] : ((((X0 @ X1)) = ((X0 @ X2))) & (X1 != X2)))),
% 0.61/0.44 inference(rectify,[],[f1280])).
% 0.61/0.44 thf(f1480,plain,(
% 0.61/0.44 ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : ((((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true) | ((((X0 @ (sK45 @ X0))) = ((X0 @ (sK46 @ X0)))) & (((sK46 @ X0)) != ((sK45 @ X0)))))),
% 0.61/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK0 @ X2 @ X1 @ X0),skolemize(X3,sK0 @ X2 @ X1 @ X0)],[f1479])).
% 0.61/0.44 thf(f1624,plain,(
% 0.61/0.44 ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) != ((paraco1147068288nge_tv @ f @ X1))) | (X0 = X1))),
% 0.61/0.44 inference(rectify,[],[f1129])).
% 0.61/0.44 thf(f1924,plain,(
% 0.61/0.44 ( ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : ((((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true) | (((sK46 @ X0)) != ((sK45 @ X0)))) )),
% 0.61/0.44 inference(cnf_transformation,[],[f1480])).
% 0.61/0.44 thf(f1925,plain,(
% 0.61/0.44 ( ! [X0 : (paraco1605129243lle_tv > paraco1605129243lle_tv)] : ((((X0 @ (sK45 @ X0))) = ((X0 @ (sK46 @ X0)))) | (((inj_on772319074lle_tv @ X0 @ top_to1057771083lle_tv)) = $true)) )),
% 0.61/0.44 inference(cnf_transformation,[],[f1480])).
% 0.61/0.44 thf(f2056,plain,(
% 0.61/0.44 (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) != $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f976])).
% 0.61/0.44 thf(f2119,plain,(
% 0.61/0.44 ( ! [X0 : paraco1605129243lle_tv,X1 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) != ((paraco1147068288nge_tv @ f @ X1))) | (X0 = X1)) )),
% 0.61/0.44 inference(cnf_transformation,[],[f1624])).
% 0.61/0.44 thf(f2748,definition,(
% 0.61/0.44 spl185_34 <=> (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl185_34])],[avatar_definition])).
% 0.61/0.44 thf(f2750,plain,(
% 0.61/0.44 (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) != $true) | spl185_34),
% 0.61/0.44 inference(avatar_component_clause,[],[f2748])).
% 0.61/0.44 thf(f2751,plain,(
% 0.61/0.44 ~spl185_34),
% 0.61/0.44 inference(avatar_split_clause,[],[f2056,f2748])).
% 0.61/0.44 thf(f2787,plain,(
% 0.61/0.44 (((sK46 @ (paraco1147068288nge_tv @ f))) != ((sK45 @ (paraco1147068288nge_tv @ f)))) | ($true != $true) | spl185_34),
% 0.61/0.44 inference(superposition,[],[f2750,f1924])).
% 0.61/0.44 thf(f2788,plain,(
% 0.61/0.44 (((sK46 @ (paraco1147068288nge_tv @ f))) != ((sK45 @ (paraco1147068288nge_tv @ f)))) | spl185_34),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f2787])).
% 0.61/0.44 thf(f2790,definition,(
% 0.61/0.44 spl185_42 <=> (((sK46 @ (paraco1147068288nge_tv @ f))) = ((sK45 @ (paraco1147068288nge_tv @ f))))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl185_42])],[avatar_definition])).
% 0.61/0.44 thf(f2792,plain,(
% 0.61/0.44 (((sK46 @ (paraco1147068288nge_tv @ f))) != ((sK45 @ (paraco1147068288nge_tv @ f)))) | spl185_42),
% 0.61/0.44 inference(avatar_component_clause,[],[f2790])).
% 0.61/0.44 thf(f2793,plain,(
% 0.61/0.44 ~spl185_42 | spl185_34),
% 0.61/0.44 inference(avatar_split_clause,[],[f2788,f2748,f2790])).
% 0.61/0.44 thf(f2814,plain,(
% 0.61/0.44 ( ! [X0 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) != ((paraco1147068288nge_tv @ f @ (sK46 @ (paraco1147068288nge_tv @ f))))) | (((sK45 @ (paraco1147068288nge_tv @ f))) = X0) | (((inj_on772319074lle_tv @ (paraco1147068288nge_tv @ f) @ top_to1057771083lle_tv)) = $true)) )),
% 0.61/0.44 inference(superposition,[],[f2119,f1925])).
% 0.61/0.44 thf(f2816,plain,(
% 0.61/0.44 ( ! [X0 : paraco1605129243lle_tv] : ((((paraco1147068288nge_tv @ f @ X0)) != ((paraco1147068288nge_tv @ f @ (sK46 @ (paraco1147068288nge_tv @ f))))) | (((sK45 @ (paraco1147068288nge_tv @ f))) = X0)) ) | spl185_34),
% 0.61/0.44 inference(forward_subsumption_resolution,[],[f2814,f2750])).
% 0.61/0.44 thf(f2819,plain,(
% 0.61/0.44 (((sK46 @ (paraco1147068288nge_tv @ f))) = ((sK45 @ (paraco1147068288nge_tv @ f)))) | spl185_34),
% 0.61/0.44 inference(equality_resolution,[],[f2816])).
% 0.61/0.44 thf(f2820,plain,(
% 0.61/0.44 $false | (spl185_34 | spl185_42)),
% 0.61/0.44 inference(forward_subsumption_resolution,[],[f2819,f2792])).
% 0.61/0.44 thf(f2821,plain,(
% 0.61/0.44 spl185_34 | spl185_42),
% 0.61/0.44 inference(avatar_contradiction_clause,[],[f2820])).
% 0.61/0.44 cnf(s36, plain, ~spl185_34, inference(sat_conversion,[],[f2751])).
% 0.61/0.44 cnf(s44, plain, spl185_34 | ~spl185_42, inference(sat_conversion,[],[f2793])).
% 0.61/0.44 cnf(s46, plain, spl185_34 | spl185_42, inference(sat_conversion,[],[f2821])).
% 0.61/0.44 cnf(s47, plain, spl185_42, inference(rat,[],[s46,s36])).
% 0.61/0.44 cnf(s49, plain, $false, inference(rat,[],[s44,s47,s36])).
% 0.61/0.44 thf(f2822,plain,(
% 0.61/0.44 $false),
% 0.61/0.44 inference(avatar_sat_refutation,[],[s49])).
% 0.61/0.44 % SZS output end Proof for theBenchmark
% 0.61/0.44 % (279125)------------------------------
% 0.61/0.44 % (279125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (279125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (279125)CaDiCaL version: 2.1.3
% 0.61/0.44 % (279125)Termination reason: Refutation
% 0.61/0.44 % (279125)Time elapsed: 0.084 s
% 0.61/0.44 % (279125)Peak memory usage: 15 MB
% 0.61/0.44 % (279125)Instructions burned: 174 (million)
% 0.61/0.44 % (279117)Success in time 0.148 s
% 0.61/0.44 % Vampire exiting
%------------------------------------------------------------------------------